A Biophysical Reaction-Diffusion Framework for Conditional Sub-Threshold Compartments in Solid Tumors: An Exploratory Translational Model
Year: 2026
Type: preprint
Abstract: Background: In early-stage EGFR-mutated non-small cell lung cancer (NSCLC), 36 months of adjuvant osimertinib significantly prolongs disease-free survival (ADAURA trial). Longitudinal minimal residual disease data provide a clinical context for studying recurrence after planned treatment discontinuation, but a post-discontinuation fraction of events is not itself an estimate of hazard or proof of biological rebound. The present work examines whether spatial transport assumptions generate a testable explanation for residual disease; it does not infer cytostatic dormancy from the clinical data. Methods: We established a multi-scale biophysical reaction-diffusion framework coupling Starling-Darcy fluid mechanics, Stokes-Einstein tissue transport, and modified cylindrical Bessel functions of the second kind ( K 0) to define the spatial limits of pharmacological penetration across tumor cords. The model uses a provisional free fraction ( f u = 0.053), trough concentration (C trough = 540 nM ), in-vitro IC50 (10.0 nM ), and explicitly assumed transport and clearance parameters. Published cohorts were used as contextual benchmarks and plausibility checks, not as independent clinical validation of the model. We also defined explicit boundary conditions under which the one-dimensional model should fail.2 Results: Under the baseline assumptions, the model gives D eff = 59.29 μ m / s , an elimination rate k = 1.51× 10− 4 s−1, and penetration length λ = 627.6 μ m . The analytical threshold crossing is r crit = 165.89 μ m , compared with an assumed oxygenated viability limit of r ox = 200.0 μ m . Under these assumptions, the calculated sub-therapeutic annulus is Δ r = 34.11 μ m , corresponding to 31.28 % of the viable cylindrical cord volume. Sensitivity analysis is reported as a scenario analysis rather than a complete uncertainty interval. These outputs are model-derived quantities, not direct measurements of drug concentration or residual disease in human tumors. Adversarial stress-testing identified invasive margins, the central nervous system, potency collapse, and low-shedding lesions as boundary conditions requiring different models or additional data. CRI = 0.47 S + 0.33 G + 0.20 M We outline SG-ADAURA as a conceptual future study question; no trial registration, sample size, randomization, or treatment assignment is proposed in this manuscript. Conclusions: The framework generates a testable hypothesis that tissue transport and geometry may contribute to incomplete eradication of microscopic EGFR-mutant disease. It defines a conditional sub-threshold compartment under explicit model assumptions; it does not establish a causal sanctuary mechanism, validate the CRI as a clinical score, or support treatment recommendations without prospective testing.
Source: Research Square
Author: Luca Celebrano
Institution: University of Naples Federico II
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225338349